In this section, we study the contribution of subdominant modes to the BH-condensate evolution and the GW emission luminosity. Particularly, we focus on the limit \(M\mu \lesssim 1\) , in which region the use of NLO analytic approximation for \(\omega _I\)  is qualified [1]}. Two dominant modes (\(\lbrace 0,1,1\rbrace \)  and \(\lbrace 0,2,2\rbrace \) ) and two subdominant modes (\(\lbrace 1,1,1\rbrace \)  and \(\lbrace 1,2,2\rbrace \) ) are considered. We first carefully calculate the evolution of the BH-condensate system without accretion in Sec. REF , then argue the effect of accretion in Sec. REF , with the help of the results in Ref. [2]}. Finally, we discuss the nonlinear effects briefly in Sec. REF .
